MCQ
A weight hangs by a spring $\&$ is caused to vibrate by a sinusoidal force .

Its displacement s$(t)$ at time $t$ is given by an equation of the form, $s(t) =$ $\frac{A}{{{c^2}\, - \,\,{k^2}}}$ $(sin\, kt - sin \,ct) $

where $A, c \& k $ are positive constants with $c \ne k,$ then the limiting value of the displacement as $c \to k$ is 

  • A
    $\frac{{ - \,At\,\,\,\sin \,kt}}{{2k}}$
  • B
    $\frac{{  \,At\,\,\,\sin \,kt}}{{2k}}$
  • C
    $\frac{{  \,At\,\,\,\cos \,kt}}{{2k}}$
  • $\frac{{ - \,At\,\,\,\cos \,kt}}{{2k}}$

Answer

Correct option: D.
$\frac{{ - \,At\,\,\,\cos \,kt}}{{2k}}$
d

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